, Volume 133, Issue 1, pp 1-17
Date: 14 Jul 2005

Weak convergence of random p-mappings and the exploration process of inhomogeneous continuum random trees

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Abstract

We study the asymptotics of the p-mapping model of random mappings on [n] as n gets large, under a large class of asymptotic regimes for the underlying distribution p. We encode these random mappings in random walks which are shown to converge to a functional of the exploration process of inhomogeneous random trees, this exploration process being derived (Aldous-Miermont-Pitman 2004) from a bridge with exchangeable increments. Our setting generalizes previous results by allowing a finite number of “attracting points” to emerge.

Research supported by NSF Grant DMS-0203062.
Research supported by NSF Grant DMS-0071468.